Abstract
Electroweak radiative corrections to the production of high-multiplicity final states with several intermediate resonances in most cases can be sufficiently well described by the leading contribution of an expansion about the resonance poles. In this approach, also known as pole approximation, corrections are classified into separately gauge-invariant factorizable and non-factorizable corrections, where the former can be attributed to the production and decay of the unstable particles on their mass shell. The remaining non-factorizable corrections are induced by the exchange of soft photons between different production and decay subprocesses. We give explicit analytical results for the non-factorizable photonic virtual corrections to the production of an arbitrary number of unstable particles at the one-loop level and, thus, deliver an essential building block in the calculation of next-to-leading-order electroweak corrections in pole approximation. The remaining virtual factorizable corrections can be obtained with modern automated one-loop matrix-element generators, while the evaluation of the corresponding real photonic corrections can be evaluated with full matrix elements by multi-purpose Monte Carlo generators. Our results can be easily modified to non-factorizable QCD corrections, which are induced by soft-gluon exchange.
Highlights
With very few exceptions, all interesting fundamental particles are unstable and can only be reconstructed after collecting their decay products in detectors
Many interesting particle processes at present and potential future high-energy colliders share the pattern of producing several unstable particles in intermediate resonant states which decay subsequently, thereby producing final states of high multiplicities
In spite of the smaller cross sections of high-multiplicity processes, predictions for those processes have to include radiative corrections of the strong and electroweak interactions at next-to-leading order, in order to reach a precision of about 10%, or better since both types of corrections are generically of this size or even larger in the TeV range
Summary
All interesting fundamental particles are unstable and can only be reconstructed after collecting their decay products in detectors. The pole scheme suggests to isolate the gauge-invariant residues of the resonance poles and to introduce propagators with complex masses M only there, while keeping the remaining parts untouched Restricting this general procedure to resonant contributions defines the pole approximation (PA), which is adequate if only the off-shell behaviour of cross sections near resonances is relevant, but contributions deep in the off-shell region are negligible. The remaining resonant contribution in the PA furnish the non-factorizable corrections They result from the fact that the infrared (IR) limit in loop diagrams and in real emission contributions and the procedure of setting particle momenta on their mass shell do not commute with each other if the on-shell limit leads to soft IR singularities. The appendices provide more details about the derivation of our central results as well as supplementary formulas that are helpful in the implementation of our results in computer codes
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